Parallel Axis Theorem: common shapes

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Name	Status	Author	Last Modified
Parallel Axis Theorem: common shapes	Ready to use	William Haynes	26/09/2021 14:27
Katrin's copy of Parallel Axis Theorem	draft	Katrin Thomson	03/06/2019 11:53

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Question statement

{geogebra_applet('j25dzmbq', [["A",A],["shape",index +1],["axis",axis],["reference",ref]])}

Write an expression for the moment of inertia with respect to the {if(axis=1,"centroidal ","")}x axis for the {shape} with {description}.

Give any introductory information the student needs.

			Name	Type	Generated Value

shape	string	semicircle
area	expression	pi*r^2/2
description	string	radius <i>r</i>
Ibar	expression	0.1098*r^4
up	expression	r - 4r/(3pi)
quadrant	integer	0
down	expression	4r/(3pi)
d	expression	c - (r - 4r/(3pi))
Ix	string	0.1098r^4+ pir^2/2*(c - (r -

			Name	Type	Generated Value

A	vector	vector(2,3)
index	integer	3
axis	integer	4
ref	integer	3
names	list	List of 5 items
areas	list	List of 5 items
Ibars	list	List of 5 items
maximums	list	List of 5 items
even_quadrant	boolean	true
minimums	list	List of 5 items
distances	list	Nested 5×4 list

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
names[index]

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `string`

semicircle

← Depends on:

index
names

→ Used by:

Statement

Parts

Gap-fill
1. Gap MOI Mathematical expression
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$\var{if(axis=1,latex("\\bar\{I\}_x"), latex("I_x"))}=$ MOI

Note: If your answer produces an error message, try putting an asterisk before parentheses, like so: b h * (h/2)^2

$I_x=\simplify{{expression(Ix)}}$

Advice

Some cases are found in the table below. For others use the parallel axis theorem.

\[I = \bar{I} + A d^2\]

where:

$\bar{I}$ is the centroidal moment of inertia, i.e., the moment of inertia of the shape with respect to an axis which is parallel to the desired axis and passes throught the shape's centroid.

$A$ is the area of the shape.

$d$ is the distance between the desired axis and the parallel centroidal axis.

Give a worked solution to the whole question.

URL
URL

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This question is used in the following exams:

Test Statics Exam by Keith Tarnowski in Keith's workspace.
Chapter 10 Exercises by Michael Proudman in Engineering Statics.
24. Parallel Axis Theorem by Michael Proudman in Engineering Statics.
Chapter 10 Exercises by William Haynes in Engineering Statics.
24. Parallel Axis Theorem by William Haynes in Engineering Statics.

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William Haynes 5 years, 9 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 6 years, 4 months ago

William Haynes 6 years, 4 months ago

William Haynes 6 years, 4 months ago

Error in variable testing condition

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Generated value: `string`

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Parallel Axis Theorem: common shapes

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 5 years, 9 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 6 years, 4 months ago

William Haynes 6 years, 4 months ago

William Haynes 6 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`